code: def laf_to_boundary_points(LAF: Tensor, n_pts: int = 50) -> Tensor:
      """Convert LAFs to boundary points of the regions + center.
  
      Used for local features visualization, see visualize_laf function.
  
      Args:
          LAF: :math:`(B, N, 2, 3)`
          n_pts: number of points to output.
  
      Returns:
          tensor of boundary points LAF: :math:`(B, N, n_pts, 2)`
      """
      KORNIA_CHECK_LAF(LAF)
      B, N, _, _ = LAF.size()
      pts = concatenate(
          [
              sin(torch.linspace(0, 2 * math.pi, n_pts - 1)).unsqueeze(
                  -1
              ),
              cos(torch.linspace(0, 2 * math.pi, n_pts - 1)).unsqueeze(
                  -1
              ),
              torch.ones(n_pts - 1, 1),
          ],
          dim=1,
      )
      # Add origin to draw also the orientation
      pts = (
          concatenate([tensor([0.0, 0.0, 1.0]).view(1, 3), pts], dim=0)
          .unsqueeze(0)
          .expand(B * N, n_pts, 3)
      )
      pts = pts.to(LAF.device).to(LAF.dtype)
      aux = tensor([0.0, 0.0, 1.0]).view(1, 1, 3).expand(B * N, 1, 3)
      HLAF = concatenate(
          [LAF.view(-1, 2, 3), aux.to(LAF.device).to(LAF.dtype)], dim=1
      )
      pts_h = torch.bmm(HLAF, pts.permute(0, 2, 1)).permute(0, 2, 1)
      return convert_points_from_homogeneous(pts_h.view(B, N, n_pts, 3))
  
imports: import math
  from typing import List, Optional, Tuple, Union
  import torch
  import torch.nn.functional
  from kornia.core import Tensor, concatenate, cos, sin, stack, tensor, zeros
  from kornia.core.check import KORNIA_CHECK_LAF, KORNIA_CHECK_SHAPE
  from kornia.geometry.conversions import angle_to_rotation_matrix, convert_points_from_homogeneous, rad2deg
  from kornia.geometry.linalg import transform_points
  from kornia.geometry.transform import pyrdown
label_desc: Use image node_id 10 for calling a global function with example usage: laf_to_boundary_points(LAF, n_pts) and returns: convert_points_from_homogeneous